The 25-year-old midfielder has been on the treatment table since he suffered the problem during Arsenal’s 4-3 defeat to Liverpool on the opening weekend of the Premier League season.
As a result, Wales manager Chris Coleman has left Ramsey out of the squad, while Jonny Williams is also missing due to a lack of match fitness.
There is also no place for George Williams , but Shaun MacDonald has received a call-up for qualifiers against Austria and Georgia on October 6 and 9 respectively.
Wales kicked off their qualifying campaign with a 4-0 victory over Moldova earlier this month.
Wayne Hennessey, Danny Ward, Owain Fon Williams, Ben Davies, James Chester, James Collins, Paul Dummett, Chris Gunter, Ashley Richards, Neil Taylor, Ashley Williams, Joe Allen, David Edwards, Emyr Huws, Andy King, Tom Lawrence, David Edwards, Joe Ledley, Shaun MacDonald, Gareth Bale, Simon Church, David Cotterill, Hal Robson-Kanu, Sam Jokes